Very Large Array (VLA) observations of the neutral hydrogen (HI) gas in two nearby edge-on spirals (NGC 4565 and NGC 891) successfully resolve the thickness of the gas layers in both disks over a wide range in radii. The combination of B, C, and D array data produces a 4 arcsec (approx. 200 pc) beam and 21 km s(exp -1) velocity resolution, combined with sensitivity to structures as large as 18 arcmin (approx. 54 kpc). These observations directly constrain the mid-plane disk mass densities, under the assumption of an equilibrium between the thermal pressure of the gas and the gravitational attraction of the disk. The results of a preliminary analysis are given regarding the z-velocity dispersion of the gas, the mass-to-light ratio of the disk in NGC 4565, and the roles of atomic and molecular gases. The data also allow a detailed study of the HI in these galaxies; in general their brightness temperature distributions seem similar to that in the Milky Way. Both galaxies show asymmetric HI extensions beyond the optical disk. In NGC 4565 the extension is a surprisingly abrupt warp, which may bend back to parallel the galactic plane; the velocity structure implies the warp is continuous around the disk.